text:
Do modern aircraft require rudder input in order to perform a coordinated turn?
With today's state-of-the-art electronic systems in modern aircraft, do aircraft equipped with autopilot systems, still require pilot rudder input to keep a turn coordinated?
For the context, I'm assuming the pilot is hand-flying the aircraft so the autopilot must be at least partially disengaged to let the pilot manually initiate and perform the turn via the yoke/stick, but still make the rudder use unnecessary or optional.
For example, would an F-16 pilot still need to apply the rudder during a turn? If the military case is not generic enough, how about an airliner pilot? Or a GA aircraft like the Cirrus SR22?

Most transport aircraft use yaw damper systems to take care of minor rudder inputs.  Most autopilot systems are actually only 2-axis - pitch and roll since the rudder's job is only to keep the tail lined up behind the nose.  The yaw damper is a separate "autopilot" system and has limited authority, sufficient to deal with minor yaw disturbances, dampen dutch roll, and counter adverse yaw from the ailerons and is active all the time whether the autopilot is on or not.
With a Y/D system the only time a pilot really needs to make a rudder input in flight is if an engine quits, because the yaw damper's authority is not sufficient to counter asymmetric thrust.  Generally in a jet, once through the departure profile, feet are on the floor even when hand flying.  They are only on the pedals to steer the nosewheel during the takeoff and be ready in case an engine quits.
On a swept wing aircraft the yaw damper is essential; if the yaw damper is off and yaw disturbances occur, dutch roll motions can start and if the pilot tries to respond with rudder inputs he almost always can't stay in phase and things get exciting.  Because of this criticality the Y/D is usually dual channel.  One of the tests done on production aircraft is to induce a large yaw movement with both YD channels off to get a dutch roll going, then engage each YD channel and make sure it stops the dutch roll.

Yaw dampers or any stability augmentation system, like pitch dampers or yaw dampers have nothing to do with coordination of a turn, they only dampen or reduce oscillations in that axis of motion due to disturbances.

No.  The Y/D system senses slip or skid and operates the rudder, within a limited range, usually around 1/4 of the total available travel, to eliminate slip or skid.  Whether it's damping yaw oscillations from a disturbance or reacting to adverse yaw it's the same.  The Y/D system doesn't care WHAT created a slip or skid, it just does whatever it has to do to center the ball/brick.  If you roll into a turn and the aileron displacement yaws the nose away from the roll a bit, the Y/D system senses the sideslip and moves the rudder to eliminate the slip.  You do not need to touch the rudder.

A bit of an exception: Airbus aircraft are full 3-axis autopilots. The rudder control has a separate turn coordination function that feeds forward roll into the rudder, and on FBW, a sideslip function to automatically stabilize the aircraft during engine failure. A major reason behind the complexity is to dampen the longitudinal flex modes of the fuselage, so the aircraft can be longer and less rigid without causing everybody in the back to get airsick.

Actually, in spite of the fact that common usage is to describe it as a Yaw or sideslip compensator, it does not do that. It senses yaw rate and applies rudder to oppose that yaw rate. It is a yaw rate stability augmentation system.  If you establish a fixed, stable sideslip angle with the rudder, the yaw damper will not oppose it. It dampens yaw oscillations not yaw.

With no rudder input from the pilot, a yaw dampener will act to oppose the yaw oscillations we call dutch roll, but if you just attempt to roll into a bank by applying aileron, the adverse yaw from the ailerons will not be opposed by a yaw dampener. Only the yaw rate (while the sideslip is being established) will be counteracted. Once the sideslip has been established, the yaw dampener inputs go away and the sideslip will remain.

@CharlesBretana One of the 747 captains around here disagrees

@dasdingonesin, What any FBW system does to control surfaces in response to pilot commands is a complex process, and not germane to a discussion about an independent system referred to as a dampener. In a FBW system both Stability augmentation, (in all axis), and flight control inputs to minimize the effects of adverse yaw, can both be part of the overall FBW algorithms.  But this word alone, (dampen), in the name for this system, should tell you what it is. It *dampens" oscillations, it does not compensate for a static condition like sideslip.

You're both right. On the 747, the Y/D responds only to yaw rate (oscillations), unless the flaps are down, in which case it also coordinates turns.

@CharlesBretana There is no FBW in a 747-100/-200. Did you read Terry's comment? If I understand it correctly, it directly contradicts what you and Peter are saying. I choose to believe him, as a (retired) captain, he should know what his flight controls are doing.

@dasdingonesin, Although I know nothing about the 747,  Peter's comment certainly sounds correct. The "system" referred to as Yaw Dampener Y/D could very easily be designed to also include functionality to coordinate turns, but that, if it exists, is NOT yaw dampening. Yaw dampening is that which opposes oscillations, not sideslip, just as we could easily add stall warning to a Fly By Wire system. But existence of a Fly by Wire system with stall warning is not proof that all FBW systems are stall warning systems.

@JohnK As mentioned by Charles in his comment above, YD is not the appropriate function for coordinated turn. A Turn Coordination function is required and is generally "separated" from the YD function. Classical YD uses uses yaw rate as feedback, which actually makes turn coordination worse.

@Jimmy but in the end the YD works to eliminate lateral acceleration and just does whatever it has to do to keep the brick centered.  When I started flying RJs I had to make a conscious choice to put my feet on the floor and stop squeezing rudder with aileron when hand flying.  I've flown with both YD channels off, and there is noticeable adverse yaw; none with YD on.

@JohnK More robust YD uses both lateral acceleration and yaw rate as feedback, so it has the capability to reduce adverse yaw once skid appears. However, Turn Coordination is usually a feedforward designed to suppress adverse yaw right off the start to increase responsiveness. If the roll rate is small, YD can do the job; for larger roll rate, feedback alone is probably inadequate.

@Jimmy yes if you make snappy roll inputs the YD will lag somewhat since it can't anticipate the aileron input.  The system is optimized for autopilot operation where the roll inputs are pretty gentle.  But my point in the end is the YD does take care of any adverse yaw, lag or no, and you do not use rudder while flying unless an engine fails, so there is a turn coordination function.  Otherwise, you would have to use your feet to keep the brick centered while maneuvering.

In my Cessna Cardinal, the rudder is cross coupled to the yoke through some kind of spring/bungey cord system (I don't have the manual handy), so I can fly with my feet off the pedals most of the time.  That's from a 1968 design, keeping turns coordinated with no autopilot needed.

+1 and yes, I'm aware of that, but I assume there is a good reason for anything that is not popular in aviation, so I guess there was a reason that that design didn't really take off too. That's why I directed my question toward autopilot systems.

@Mahdi By definition, the design had to take off... it is not an aircraft if it never takes off. :)

Which design? The Cessna Cardinal, or the smooth flying that the interconnected rudder offers? Maybe other non-autopilot equipped planes offer similar.

@CrossRoads I was talking about the interconnected rudder. I have heard of a very few other similar designs, but there should be a reason that is not adapted in most other aircrafts.

@CrossRoads BTW, I'm not saying it's a bad idea or it won't work! I'm just thinking that there must be a reason that that design is not very popular, possibly some added design complexity drawbacks.

I don't think you can say it's not popular without hearing from other GA pilots.

There was also the Ercoupe, which didn't have pedals at all. But it is true that for some reason the design never became massive. Personally, an aircraft where I cannot sideslip would make me uncomfortable; and although it is supposedly impossible to enter a spin, it would make me nervous.

What year was your Cardinal?  I owned a '68 and it didn't have an interconnect.  What that on the RG?

Mine is a '73 FG.

@CrossRoads Sorry I meant 'popular' between manufacturers -- in terms of interconnect design. I believe Richard Collins used to own a Cardinal RG before his P210 and I have no doubts he had a lot of reasons for owning one.

@Mahdi: Perhaps the reason is that most private pilots learn to fly in aircraft that don't have such systems, so that use of the rudder becomes natural.  If you then go to a system that eliminates the rudder, you have to consciously think about it.  I would think it would be like me trying to drive a car with automatic transmission: unless I pay close attention, I automatically try to use the clutch, and often wind up stepping hard on the brake instead.

The need for rudder to coordinate a turn is directly dependent on Angle of Attack (AOA). At positive angles of attack, the down aileron is more in the relative wind than the Up aileron (due to blanking by the wing in front of the aileron). An aircraft that is at zero AOA, (like a fighter unloaded, in a zero-G ballistic arc) requires no rudder. To avoid this problem, in modern aircraft, like the F-15, for example, differential stabilator is used to mitigate this issue. The stick is mechanized so that the further aft it is, the more any lateral motion is directed to generating asymmetrical stabilator deflection, rather than aileron deflection. SO, at high AOA (assuming that stick position is an accurate indicator of AOA), when the pilot moves the stick to the side, the ailerons deflect very little or not at all, but the stabilators at the tail deflect asymmetrically.
The F-16 flight control surfaces are completely computer controlled, so pilot inputs are interpreted as commands for aircraft movement. The computer then determines, based on all known factors (AOA, Airspeed, etc.) what to do with all control surfaces (including the leading and trailing edge flaps) to get the airframe to move in the manner commanded by the flight control inputs.
I never flew the F-16, (perhaps someone who did can clarify), but my guess is that there is no need to depress the rudder pedal in the F-16 to coordinate a turn - that the computer automatically determines how much rudder, or differential stabilator, should be deflected to coordinate the requested roll rate.

In this podcast around 0:57 the F-16 pilot says 90% of a mission he will not use the rudder, it flies coordinated without input.

An interesting corollary to this is that early in the F-16's operational deployment, an aircraft was lost due to something called Inertial Roll-Coupling. Common practice in Air-to-Air training when adversaries were on different frequencies (like in a Red-flag type major exercise) in order to acknowledge you were aware of an attack from an adversary, was to perform a rapid wing-rock, rolling the aircraft rapidly back and forth through a large range of bank angles.  Apparently the Engineers did not include this scenario in the FBW algorithms, and an aircraft at Nellis was lost as a result.

I once spent a couple hours flying a full-motion 737 simulator with an instructor for that type. My previous flight experience comprised entirely one hour at the controls of a Cessna 180 (cruise only) and hundreds of hours of Microsoft Flight Simulator with just a joystick, so I was pretty excited to show off that I knew, in theory, what a coordinated turn is. The very first flight set us up in a situation necessitating a decisive turn to enter the traffic pattern correctly. Being somewhat overwhelmed (hand-flying a 737 in a real sim is a fairly big leap from on a desktop computer), I of course completely forgot I had rudder pedals until halfway through the turn. The moment I even brushed my foot onto one, the instructor said, and I remember this exactly, "woah there; we only use those if we want to make all the passengers sick!" We continued the session hand-flying approaches in all kinds of weather in all kinds of places. I never once needed to touch the rudder pedals again.
The modern Boeing jets all have the ability to use their yaw-damper systems to coordinate turns (although turn coordinating is physically not the same as yaw damping). The details of the implementation depend on the model. For example, 747s coordinate turns only with the flaps down, while 777s and C-17s always do.
Boeing also has a design philosophy known as the "tameness criterion", which dates back to the 707 program. This rule necessitates an aerodynamic design that allows control to be maintained with only the ailerons in asymmetric-thrust conditions, up to and including one engine out. (There are more specific restrictions that vary among models.) The rudder cannot be used at all to meet the requirement, even by the autopilot. While a turn in this condition may not strictly be "coordinated", the design of the big jets takes into account a successful turn without rudder.


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What is the difference between Line-Replaceable Unit (LRU) and Integrated Modular Avionics (IMA)?
I'm studying the Integrated Modular Avionics (IMA) and the Line-Replaceable Unit (LRU), but I don't get the difference.

A Line Replaceable Unit is a piece of hardware that can be exchanged for a replacement part in a relatively short time by only opening and closing fasteners and connectors. You will find the term LRU in avionics but also in ATC hardware. Examples are FMC, transponder, etc.
When you have a complex avionics system you tend to end up with a great variety of LRUs. All these LRU have a very specific function. To be able to quickly replace malfunctioning parts, maintenance needs to keep a large stock of spares for all these LRU's.
The Integrated Modular Avionics concept attempts to reduce the variety of LRU's by designing the avionics with common components. E.g. one type of power supply, one type of memory unit, one type of processing board and only a few variations of input/output modules. Instead of working with very function-specific LRUs, the IMU works with more generic Line Replaceable Modules (LRMs). This reduces the number of replacement parts that need to be kept on stock. The LRMs of IMA have more generic functions than in a traditional avionics system.

Very clear, thank you. I have another question regarding IMA, if you can help me: System development and integration procedure for IMA

An IMA is a computer network utilising the ARINC bus system that interconnects various devices. This is in contrast to Line Replaceable Units LRU'S where they are standalone systems that can be replaced. Basically they are electronic boxes typically in the aircrafts electronics bay that can be swapped out quickly. Because they can be swapped out quickly they can be done on the line. Ie. When the airplane is on the tarmac or in the hangar

IMA is designed with various replaceable modules that can be swapped out quickly. Both the systems have this characteristic in common, isn't it? May I say that IMA uses LRU, and each unit is a Module?

Yes but the whole system cannot be replaced easily. Cards can be removed but the underlying system will still be there.

Also it is easier to deal with LRU'S in troubleshooting because you would just replace the whole unit. Less troubleshooting.

They decided to substitute the old computers with LRU, easily replaceable. In a second moment they decided to put everything in a single computer, not replaceable, but partitioned into many modules, featuring the decomposition of the avionic devices into its basic functional elements. Am I right? IMA is younger than LRU, isn't it?

A lot of the LRU'S do not have computers. I worked on a lot of LRU'S that just have analog devices in them. Ie transformers, wiring circuits that distribute power etc... so not all LRU'S have computers in them.

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How does stall depend on angle of attack but not speed?
Everyone says that the angle of attack is what determines a stall, not the speed. I understand the theory and understand that it is separation of the airflow that matters for stalling.
However, I don’t understand in a practical sense. Let’s say you’re in a Citabria going at 100 knots. If you pull up extremely fast, you can get a high angle of attack, beyond what you’d need to stall at 60 knots, yet you wouldn’t stall straight away. If you stayed at that angle of attack, you’d quickly slow, then stall. But if I’m right that you wouldn’t stall straight away, then it seems like the angle of attack is not the only thing that matters.
What am I missing? What’s wrong in my argument?

If only the angle of attack would have been what was determining stall, I don't think the Apollo program would have been especially successful :)

@Speldosa AoA is the only thing which determines a stall. Though I'm not sure how that relates to the Apollo program.

@Speldosa: pitch angle is not the same as the angle of attack, I don't think.

This would be a wonderful question to answer with an animated gif.

@Speldosa: Stall does not remove all lift. Part of lift is caused by reduced pressure over the upper surface and part by increased pressure under the lower surface. And only the first part goes away stall. Because the reentry is hypersonic, Apollo didn't need any pre-stall lift. The upper surface wasn't suitable for generating it anyway.

Why did Apollo need any lift at all, exactly?

to maneuver the capsule up/down in the reentry corridor, and to adjust for the desired landing spot. Capsule simply had an offset CP vs CG producing a small amount of (negative) lift. No idea how this is related to the OP's question...

@BretCopeland: I believe you mean "The only thing at the subsonic speed of the Citabria" because the critical Mach number also plays a role in stall, solely determined by Mach speed. I posted an answer to explain

In the thoroughly subsonic flight regime:  If a-o-a is not one of your specified parameters, then stall certainly does depend on airspeed, in combination with other variables.  However, if a-o-a is specified, then there's no role left for airspeed to play-- with the wing at any given angle-of-attack, airspeed plays no role in determining whether the wing is stalled or not.  Either the wing is at the stall angle-of-attack, or it isn't, period.  (This probably should be an answer not a comment-- I'll work on making it into an answer.)

I believe you are confusing the wing angle of attack with the pitch of the aircraft.  Aircraft moving at a slow, near-stall speed, despite pointing the nose up, will still be traveling more or less horizontally.  Their VSI instrument will read near zero.  Whereas, if you take an aircraft moving quickly and pull the nose up to the same angle, the aircraft will, obviously, climb rapidly.
Why does this matter?  The angle of attack is defined based on the wing's motion through the relative wind.  The wing's orientation relative to the ground isn't involved in the definition in any way.  When the aircraft as a whole is climbing, the relative wind is coming down from above.  As a result the angle of attack is reduced, compared to what it would be if the plane were not climbing.
Just to show some quick numbers, suppose you took an aircraft moving at 100 kts in still air and pulled the nose up so that you are now climbing at 3,000 FPM (most aircraft will lose speed doing this, but the math is valid until the airplane slows down).  $1knot\approx100FPM$, so you'll now have an upward vector of 30 knots.  Your 100 kt airspeed is now moving up at an angle.  A little trigonometry:
$$\sin(x)=\frac{30}{100}$$
$$x=17.46°$$
So, your angle of attack is 17.46 degrees farther away from stalling when climbing at 3000FPM than it would be if your aircraft had the same pitch but was in level flight.
However, few aircraft have the engine power to sustain a climb at this rate.  The aircraft will bleed off speed, and as the speed bleeds off, the aircraft will slow, the climb rate will decrease, the aircraft's velocity will become closer to horizontal, and, eventually, the aircraft will stall if the pitch is held constant.

When you say "angle of attack is 17.46 degrees farther away from stalling" I think that is a bit confusing. You could clarify that that aircraft is now pitched upwards 17.46 degrees, but the angle of attack does not increase by that much. In fact, AOA would decrease, right?

super helpful answer, thanks a lot! clarified my understanding and makes sense.

I agree with @fooot, your explanation itself seems to confuse AoA and pitch in the fourth paragraph. I think what you're trying to say is that pitch has increased, but angle of attack has not, and therefore the pitch angle which can be achieved without stalling has also increased. You should also point out that, in your example, all of the climbing force is generated by increased thrust, whereas most aircraft climb using a combination of thrust and lift, and additional lift requires a higher angle of attack, or a higher airspeed (those are the two ways to generate more lift).

Unfortunately, my first comment got mangled.  What I meant to say in it was this: The explanation is right but it's possible that it could be phrased differently.  I wanted to contrast the climb scenario with the level slow flight scenario by showing that, for a given pitch, AoA is reduced in a climb.

Finally, lift is actually not increased in a climb.  It increases only momentarily, to enter the climb, but in a sustained climb, it's the same.  If you climb without changing speed, the only effect changing your AOA will be the slight influence of the lift vector no longer pointing straight up, but angled slightly aft; but part of the thrust vector will also be pointing up, so the magnitude (or even direction!) of this change will depend on the exact aircraft and parameters of the climb.  A handy way to think of it: airspeed * AoA = G-force.

I'm not disagreeing with you. I was just pointing out that, in your example, the reason the plane climbs is because of downward thrust. If you were using increased lift to climb (like most small aircraft), then it would require a higher angle of attack. I just thought it might be confusing if someone were to read that and not understand what was allowing the airplane to climb.

At the top of a vertical climb there is no stall because airspeed is zero. You cannot stall an airplane when the airspeed is zero. See any V/G diagram.

It's funny you mention a Citabria, because I've actually done exactly what you're talking about in exactly that airplane. Not that it really matters, because this will apply in any airplane.
In your question, you said that you understand angle of attack is what causes the stall. But I'm not sure that you understand that given the same wing, it's always the same angle. I say that because of this:

you can get a high angle of attack, beyond what you’d need to stall at 60 knots,

The angle of attack you need to stall remains the same, regardless of speed. Perhaps things are different in the supersonic realm, but this is good enough for Citabrias.
You're right that if you were cruising at 100kts and suddenly pulled back on the stick, you would slow down before stalling. But that's not what causes the stall. The stall is caused by high angle of attack, and that's caused by elevator position.
Stick position is the single best predictor of when an airplane will stall, and nobody talks much about it. I can also say your example isn't 100% accurate, because I've actually done it. If you cruise at 100kts, then slam the stick back as hard as you can, you'll stall with a minimal loss of speed beforehand. And if you wanted, you could have a higher entry speed than 100kts and stall at 100kts. Eventually, you get into structural issues caused by the excessive g-loading.
Stalling isn't just caused by angle of attack, it's always caused by the same angle of attack. I hope this answers your question.

Well, for the example correct answer is the part where you say "If you cruise at 100kts, then slam the stick back as hard as you can, you'll stall with a minimal loss of speed beforehand.".

If I take the 60 knots in the question, stall loading at 100 knots would be just 2.67G. But internet search gives me just 44 knots and that gives me 5.17G at 100 knots, or just a little over the structural limit. You'll probably bleed off the 2 knots to get within limit in the entry to the manoeuvre.

Yeah, the 44kts for Vs is correct. It's also important to remember that changes dramatically with weight. And the Citabria 7ECA has at least two gross weights, depending on the wing struts.

Consider the zoom maneuver. At any point in the zoom (easier as the aircraft slows), merely centering the stick will stall the airplane.

This answer should have many more up-votes, and should've been marked as the answer, unless the OP didn't actually know what he was asking.

Re "Stick position is the single best predictor of when an airplane will stall"--this is basically true, at least in linear flight, but in a turn, especially when the airspeed is low, and therefore the radius of curvature of the flight path is small, the contrl stick position at stall can be much further aft than in linear flight. This is due to aerodynamic consequences of the curvature in the flight path and relative wind. This effect can be extremely pronounced during a loop. See for example https://aviation.stackexchange.com/q/55713/34686 and https://aviation.stackexchange.com/a/55876/34686

@rbp - Re "Consider the zoom maneuver. At any point in the zoom (easier as the aircraft slows), merely centering the stick will stall the airplane. ". -- a) are you sure?  b) if so any idea why?  Is the aircraft's rotational inertia in the pitch axis playing a significant role here?  Similar to when you establish very steep climb and then chop the throttle, without pushing stick forward?

The stall Angle of Attack (AoA) is not fixed, but increases with pitch rate and - to a lesser extent - with the Reynolds Number.
When a wing stalls, the boundary layer in the rear part of a wing stops and even reverses it's flow direction, causing separation. For the outer air flow, this looks as if the wing has grown thicker there and has a smaller AoA than before, without separation. This causes the lift loss of a stalled wing. The "history" of the local boundary layer influences this - if it has seen a high acceleration around the nose of the airfoil, it has to perform a steep deceleration over the remainder of the wing. Friction has already reduced the energy of this boundary layer, and the steep deceleration ends in separation further downstream.
If the stall AoA is approached rapidly, the boundary layer on the rear wing has still the characteristics which go with the low AoA that prevailed when that parcel of air flowed around the wing's nose. Therefore, it has more energy left and is less prone to separation. The effect is an increase in the stall AoA with pitch rate, to a point where the total lift of the wing is 50% more than that at the stationary AoA at the same speed. Of course, this is a dynamic stall with a load factor much higher than 1. For more details, I refer you to NACA TN 2525 from 1951. No price for guessing which airplane was used.
On the flip side, the lift drops much more than in a static ( = slow pitch rate) stall. A docile stall behavior can now become abrupt! Another consequence of this lift overshoot is the possibility of a hysteresis loop, especially in helicopter, propeller and turbine blades where strong and cyclic changes in AoA are possible. This is called lift flutter and causes high mechanical stresses and vibration. See Sighard Hörner's "Fluid Dynamic Lift", page 4-24 and 25 for more.
The Reynolds number effect is less pronounced, but still gives an increase in stall c$_{l max}$ of 15 - 25% between $Re = 10^6$ and $Re = 5\cdot 10^6$. Details depend on the particular airfoil. Abbott-Doenhoff or the Wortmann catalog have lots of data on this.

Please bear in mind that by using a ⋅ (\cdot) to imply multiplication can be confusing to a lot of people, since it looks identical to a decimal point. \times is probably a better bet. See also this, which corroborates the ambiguity: When should \cdot be used to indicate multiplication?

+1 for the talk about pitch rate influence. Is there some relation in pitch rate vs speed where this effect becomes noticeable?

@Radu094: Yes, the pitch rate needs to go up linearly with air speed to keep the effect constant. NACA TN 2525 gives the parameter $\frac{c}{v}\cdot \frac{d\alpha}{dt}$ to calculate the maximum lift coefficient (c = wing chord). Values of that parameter up to 0.66 were tested, and the maximum lift coefficient increased linearly over the whole range. For the stationary case the parameter was generally less than 0.05.

Peter, there's no need to be so infuriated. Of course I read the link; there are answers, but there are also 2 or 3 comments/paragraphs in answers about how it is ambiguous. I'd've pinged you in chat instead, but you haven't visited it. This was more of a polite recommendation, not me trying to force something upon you. I was merely trying to help you improve clarity.

But if I’m right that you wouldn’t stall straight away

You will stall right away. You won't pitch down immediately though.
Immediately when you exceed 2.67G1, the aircraft will start to buffet and kick back somewhat as pulling more on the yoke no longer causes increase in lift and the pitch up rate and acceleration will stop increasing. But the pitch will not stop increasing. The wings are still generating some lift, just less than before stall. So you'll continue climbing until you run out of kinetic energy (which you will faster than usual because drag is increased in stall) and decelerate below the speed at which the stalled wings can't produce enough lift to balance the weight. At that point your speed will still be higher than the 60 knots, because at 60 knots the wings can balance the weight when not stalled, but in this case they are stalled already.
1Taking 100 kts cruise and 60 kts vs. Internet search gives me just 44 knots for vs and that would mean 5.17G for stall at 100 knots while the certified limit is 5G, so you shouldn't be doing it at 100 knots, only up to 98.

The foot note and the "practical sense" of the original question reminds me of "weather penetration speed": A certain speed at which the aircraft will stall before reaching it's structural limits, should it be hit by excessive air loads.

Yes, yes, yes.  Stalling doesn't mean falling.  It just means the wing is converting airspeed to lift inefficiently.  It says nothing about the entire airframe's trajectory or even its orientation.

Imagine you throw an airplane with the bottoms of the wings facing forward at 500 knots. The aircraft is going very fast, but rest assured it is stalled. It could recover very, very easily because it has so much kinetic energy and there as a huge amount of airflow, but it is not producing lift the way itshould.

Well, recovery in this situation might be somewhat complicated by the disintegration of the airframe. :)

This is a standard aerobatic manuever for model radio-control aircraft, called The Wall.  Without changing altitude, pitch up until the nose points straight up.  (Then climb vertically to regain airspeed and control authority.)

... and on the other extreme, pitch up to 60 degrees nose high, and stuff the stick forward a few inches, AND KEEP IT THERE. No matter how slow you get, the aircraft WILL NOT STALL.

It is unfortunate that more aircraft don’t have AOA indicators. In Navy aircraft, particularly carrier aircraft, it is a primary reference of critical importance.
I was a flight instructor in the Navy, and taught the out of control flight syllabus. Literally a hundred hours “flying” a stalled aircraft. While the behavior when generating very high pitch rates where you would “blow through” the stall AOA could be odd, in general all of the behaviors associated with stall ( buffet, loss of lift) occurred at the exact same AOA. We’d demonstrate this at speeds from 250 kts (6G pull) to 50 kts (vertical climb). We’d control it in beyond stall, losing 15,000 ft while demonstrating what control over the airplane you did have post-stall. Demonstrate flying the aircraft in the vertical at well below what would be stall speed for straight and level, but the plane was still flying since the G load was zero. We’d stall it upside-down at the top of a loop.
Always the same AOA.

To understand this, I like to think of a jet with afterburner pointed nearly vertical. It's not stalled, the angle of attack is nearly 0, because the relative wind is going nearly straight down due to all the thrust. But "straight down" is still going smoothly across the wings, no stall.
Similarly, a Cessna 172 going 10 kts ground speed, pitched level to the horizon, is going to be decending far faster than the 10 kts of ground speed, so the relative wind is hitting the bottom of the wing. Just another way of describing a high angle of attack.
This may only make sense in my head, but it works for me.

You wouldn't necessarily stall if you applied abrupt elevator at, say, 100kts due to there being enough inertia to ensure that the airflow relative to the chord line (AoA) did not, infact, exceed the critical angle.

Are you talking about rotational inertia in the pitch axis, or some other inertia?  Answer would benefit from clarification.

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text:
How do cross-wind correction controls help while on the ground with wings level?
When taxiing, taking off and rolling out we are told to use cross-wind correction inputs. Assuming a headwind, you bank into the wind by raising the aileron on the windward side and lowering the other aileron.
However, it appears that just before you take off, even with the wings level, holding the ailerons as above helps the plane avoid skidding sideways on its wheels. I understand the physics once you are airborne and the wings are no longer level (you will slip into the wind). But what I don’t understand is why holding up aileron on the windward side helps prevent skidding sideways, even with the wings level.
How do the physics work to prevent sideways force on the gear? Or am I imagining that the wings are level and in fact the windward wing is lowered?
I’ve felt this more strongly in a Citabria 7ECA or similar light tailwheel, high-wing aircraft, but I think it also applies to a tricycle-gear C172 or similar.

Perhaps the raised aileron provides more torque (given the aircraft’s forward speed) than the lowered aileron? That would give a net into-the-wind torque which could correct the weathervaning tendency. (But would be in the opposite direction to your theory.)

Some good points here @falstro. My question is in fact precisely whether the correction you do does prevent skidding without increasing the downward force on the wheels. It feels like it helps prevent skidding (even when the aircraft is about to lift off) but I could be wrong.

Your assumption is that the wings are level when both main wheels are on the ground. But this is not necessarily true. Even when both wheels are on the ground, the wings can still have a small tilt. The suspension of each gear works independent of the other, and the weight on the wheel determines how much the suspension compresses or the gear strut will bend. By deflecting the ailerons, you re-distribute the lift between the wings, and control gear compression.
Please note that with the ailerons level, your wing will create a sizable rolling moment in a crosswind, which means that the load distribution between the two main wheels is uneven without aileron correction. Also, the fuselage will create a side force of its own, and this force increases with speed as more of the flow around the fuselage will be attached.
The slight tilt angle of the wing also slightly tilts the lift vector, and this, together with the side force of the fuselage, creates the side force which causes the skidding when this side force is large in comparison with the low load on the wheels shortly before takeoff. You need to tilt the wing into the crosswind to create a counter-force which can compensate the side force of the fuselage, only then the whole aircraft will not experience a side force.
I know, the picture below shows a glider and not a Citabria, but the principle is the same. The high wing arrangement creates a sizable rolling moment even without dihedral.

how can it have the same local alpha distribution and opposite rolling moment?

@Federico According to whether the fuselage is masking the wind above or below the wing. In the top diagram, the high wings mean the air pressure is lower below the downwind wing; in the bottom diagram, the low wings make the air pressure lower above the downward wing.

@Federico: You are right, the diagram labels were wrong. Thanks for finding it!

the part that this answer is missing is that even without the lift of an airfoil, allowing the wind to get under the upwind wing is enough to flip the plane over. Try carrying a 4x8 piece of plywood in a crosswind. also gear compression has little if any to do with it: citabrias have unsprung gear, and gliders have none, but they are both still susceptible to flipping over in a crosswind.

@rbp: Then I ask you to walk up to a Citabria 7ECA and rock the wings. That thing will rock like a swing! The cantilevered gear struts have plenty of elasticity.

i have hundreds of hours in a citabria and its bigger brothers. sure they rock, but they don't compress, and the point is moot anyway because gliders have none.

@rbp but the wheels themselves compress a bit, having a wing span 10x the wheel base results in the wingtips moving 10x of how much the wheel compresses when the plane it rocked.

@ratchetfreak: Yes, but the gear strut bending is really the biggest contributor, adding more deflection to that caused by tire compression.

again the point about the main gear is moot, since gliders don't have any, and gliders are subject to sliding just as much. or at least lets agree that "gear compression" should be replaced with some term that includes gear that doesn't compress.

@rbp: Please ... gliders have a central wheel and effectively zero stiffness around the roll axis. The pilot alone is controlling the roll angle, and he has to do this in exactly the same way as in a plane with a two-track gear. Why should the point about the stiffness of a two-track gear be moot when the original question assumed that the gear would have unlimited stiffness?

i don't understand what "zero stiffness around the roll axis" means

@rbp: See stiffness as the capability to create a restoring force when moved. The glider wheel will not restore the level attitude once one wing is dropped, but the two-track gear will. But it allows some movement (which creates a limited restoring force, hence finite stiffness), while the question assumes that the gear will not allow the wing to drop, hence unlimited stiffness (= infinite restoring force).

re-read your first paragraph, @PeterKämpf, and explain the answer for a glider instead of a Citabria. you'll find that you can't begin the answer with "When both main wheels are on the ground..." doesn't apply because gliders don't have main wheels. that's why the main gear can't have anything to do with the answer to the question.

@rbp: Don't focus on one vs. two wheels. The question assumes that if both wheels are on the ground, the wings must be level. This is not true, and for a glider obviously so, because the single central wheel allows the wings to drop until one tip hits the ground.

asking me to ignore the difference in gear proves my point that gear doesn't matter

When taxiing in a crosswind, the fuselage blocks the airflow over the downwind wing (just as if it were in a slip), so the upwind wing has that much more lift than the downwind wing.
Also, if the wind gets under the upwind wing, it will just push the upwind wing further upwards, just as if you were carrying a 4x8 piece of plywood.
These two factors can contribute to tipping the airplane over.
With gliders, this is much more pronounced because they don't have wheels under the wings, so the ground crew always keeps the upwind wing lower in a crosswind. In a glider crosswind takeoff, full upwind aileron is applied before takeoff, and as the aircraft starts to roll, the aileron is continually reduced to keep the wings level, with downwind rudder to keep the fuselage aligned with the runway.
And now to answer your question: up aileron on the upwind wing will reduce the lift on the upwind side and increase the lift on the downwind side, to help the aircraft from sliding sideways.

The question is about side force, not tipping over. @Peter mentions a skidding motion shortly before takeoff, and that can only be explained by a side force, not a rolling moment.

good catch re slideing versus tipping. corrected. I don't have "rolling moment" anywhere in my answer. you must mean the other one.

I understand your mentioning of a lift difference as a rolling moment. Pushing one side of the wing upwards sounds awfully like a rolling motion.

there is both a horizontal and vertical component. you need enough horizontal component to counteract the wheel skidding.

I think the biggest component of the difference is the surmised answer, that is the wings are not level in the described situation. If wing is strong enough, you will have to transition to rolling on one, upwind wheel, or you will not be able to keep on the centerline.


text:
How do I obtain permission to fly in surface class E airspace under FAR-103?
I'm a paramotor pilot operating under FAR 103, and I'm trying to determine who I need to ask for permission to fly in class E airspace that extends to the surface and is designated for an airport. For reference, the particular airport that I am inquiring about is GFL.
This appears to be the relevant subpart of FAR 103: §103.17

No person may operate an ultralight vehicle within Class A, Class B, Class C, or Class D airspace or within the lateral boundaries of the surface area of Class E airspace designated for an airport unless that person has prior authorization from the ATC facility having jurisdiction over that airspace.

Before I was aware of this restriction, the airport manager granted permission for me to fly to and from the airport with my paramotor. I have an access card, and he made clear the rules I am to follow, such as radio procedures and where I can launch and land.
However, this field does not have a control tower. Do I need to obtain permission from someone else to comply with §103.17? I'm not sure who the ATC facility having jurisdiction over that airspace is.

By default, all controlled airspace (class E and up) is owned by an ARTCC. In many areas, they delegate airspace (including class E!) to other ATC facilities, either a TRACON or a Tower.
Unfortunately, that info isn't on Sectional or Terminal Charts; you have to look in the Chart Supplement (formerly Airport/Facility Directory). For KGFL, we see:

ARTCC: BOSTON CENTER
...
ALBANY APPROACH: 132.825
ALBANY DEPARTURE: 132.825

So, this area is owned by Boston ARTCC and delegated to Albany TRACON, and it helpfully gives you the latter's frequency to call if airborne.
You probably can't reach them by radio from the ground, so you would contact their Clearance Delivery (CD) by phone, which for this airport is found in the remarks:

FOR CD CTC ALBANY APCH AT 518-862-2299.

Just tell them in plain English why you're calling and what you want, and be ready to copy any instructions they give you. They might, for instance, ask you to wait because they have other traffic going in or out in the next few minutes, or they might ask you to contact them in the air so they can keep track of you (I assume they won't see you on radar) and warn other aircraft you're there. Or they might not care at all and just tell you to have a good flight.

Be sure to verify that the airport in question specifically has a "Class E Surface Area". This will be denoted by a dashed line encircling the airport on the sectional map - like a Class D in magenta instead of blue. Typical Class E airports will only be surrounded by a magenta gradient designating transition area and the Class E airspace only extends down to 700 ft above ground level, even over the airport. You don't need authorization to operate your ultralight at an airport where the Class E airspace doesn't extend down to the surface, even if you climb up into the Class E airspace.
If your airport does incorporate a Class E Surface Area, it will nearly always fall inside the magenta gradient circle, mimicking the inverted layer cake design of Class C and B airports. This is done to protect E airports with precision IFR approaches and/or departures.

All airports with a Class E Surface Area are required to have a
weather station and the ability to contact ATC from the ground. This
ATC may be Flight Service, a center facility, or an approach/departure
facility.

Most of the content above (including the direct quote) is based on content in this 2016 article by Swayne Martin, found on the "Boldmethod" website: "The logic behind class E airspace".
Whichever ATC is responsible for providing clearances on your particular airfield will be listed in your Chart Supplement US (formerly called an Airport/Facility Directory or AFD). The frequency for this facility will be listed, and it is this controller that you must contact to request clearance for your FAR 103 flight.
Hope this helps.

Please note that I'm 100% certain that the airport in question is within class E airspace that extends to the surface and is designated to said airport, and I believe the question is asked in such a manner that makes this apparent. This answer seems to ignore the actual question, and instead answer a question something like "how do I determine whether an airport is within surface class E airspace?".

I did not mean to insinuate that you, personally, don't know the status of KGFL. I thought that there might be other FAR 103 flyers who could stumble across your post looking for clarification and answers. In that case, providing a bit of additional information could help them decide what they need to do.

Edited to make clear what portion of the answer was conveying or quoting content from the Boldmethod article and what portion was not. A previous edit (not by the OP) made it look like the whole answer was directly quoting the article, which wasn't the case-- the article doesn't mention Part 103 operations at all.

I don't think that "typical Class E airport" is really the right phrase to describe an airport with Class E airspace overlying at 700' AGL (and the Boldmethod article never used that phrase), so there may be room for some further improvement here--

-- but don't wish to change OP's wording too much, as he seems to be no longer around to approve/ roll back edits --

This isn't a complete answer, but the practical answer is that you may not need to contact anyone.
I'm aware of an airport, within the surface-level Class E airspace designated for another airport, where ultralight operations are routinely conducted-- in fact an ultralight airplane manufacturer was long based there. As far as I know, no arrangement for prior authorization has ever existed. Paramotors also routinely launch from nearby fields within the same airspace. This site is on the outskirts of a major city that has a FSDO.  An FAA Examiner routinely gives checkrides at this site, and no one I've spoken with (including the Examiner) was aware that there was any requirement for prior authorization for Part 103 operations here.  (However, it may help that the field is not the same one for which the surface-level Class E airspace is designated-- rather, it is several miles distant, and is much smaller, with a much lower frequency of operations.)
So yes, you definitely do need to obtain authorization if you want to fully comply with 103.17, but if things are working for you as is, I wouldn't worry about it, especially for low-level operations.
If you do want to seek permission, it seems perhaps that some sort of standing Letter of Agreement permitting low-level operations under certain specified circumstances might work better for you than trying to telephone the ATC facility on a case-by-case basis.
While your specific question makes it clear that you want to take off and land within the airspace in question, and apparently on the grounds of the actual airport for which the airspace is designated, at least one answer has suggested that calling the ATC facility on the radio in flight might be an option in some circumstances where an ultralight pilot wishes to enter Class E airspace that extends down to the surface.  I'd suggest that pilots not do  that unless the facility has already specifically instructed them to do so.  The staff may have no idea that FAR 103.17 even exists, and might have trouble understanding exactly why they are being called.  Furthermore, they might not have a clear understanding of the vertical extent of the airspace1 in which FAR 103.17 says ultralights can't operate without prior authorization.  The situation seems ripe for confusion.
Footnotes:

For more, see the related ASE question In reference to airspace, what does the FAA mean by "within the lateral boundaries of"? Is this construed to also imply a vertical limit?

Would be interested to hear from anyone who has taken the approach suggested in second-to-last paragraph, or who has gotten good results by calling ATC on the radio in flight-- please post an answer, or ping me via "@...." in comment or chat post and we'll discuss further in chat-

While I've never contacted ATC in flight, I have been granted authorization by calling ATC prior to taking off.

There was some follow-up chat in a related chat room, starting here https://chat.stackexchange.com/transcript/message/62996132#62996132


text:
Why is a special certification needed to land at Paro Airport?
Why is Paro Airport (currently the only international airport of Bhutan) considered one of the most dangerous airports to land in the world?
Is it because of the mountains? In my opinion, Princess Juliana International Airport is also as challenging as Paro.

Why do the pilots need a special certification to land there?
How do they achieve this certificate?

I think this says it all...https://www.youtube.com/watch?v=rmGy7qcDwQU

Yeah!    It all seems calm for the first part, and then as they're closer to the ground it's like "hmmm - where's the runway", then the turn onto finals: wow!   There it is!

@User58220 Now I know that I can never be an airline pilot. Not only am I too old to learn something like that but also, I'd burst out laughing and lose concentration when, at a critical moment, the aircraft dispassionately criticized my flying: "Retard. Retard. Retard. Retard."

According to Wikipedia, The History Channel rated Princess Juliana as the fourth most dangerous airport in the world. This seems to be yet another case of that channel being more interested in sensationalization than education.

You rarely need to perform a sharp turn with precise rate of descent, bank and speed, from a precise altitude/heading, to a target altitude/heading. Attitude and motion greatly vary from one aircraft to another. Qualification for Paro also involves the airframe. You don't need that on SXM. SXM is sensational only because you can get there easily and it's well known (Gibraltar is more tricky for eg.) Who knows of Paro ? almost noone to be honest. So most of the world don't really care if Paro is special. There are some airfields in the middle of nowhere much more tricky than SXM.

@DavidRicherby: The worst thing is than the call itself is retarded. It seems to be triggered by 20 or 15 ft RA and does not check speed, so it will tell you even if you are slow on the approach and should keep power down to touch-down to avoid tail-strike (there was a tail-strike incident where this was described; I read it on avherald, but don't remember enough details to find it now).

@DavidRicherby: As for the History Channel list both the order and the choice are rather questionable. It is built more to be varied, otherwise Nepal alone probably has 10 airports more dangerous than TCNM. TCNM itself probably got into the list more due to risk of the fools hanging on to the fence than risk to aircraft themselves.

The approach to Paro is unbelievably complicated. It is flown visually through a valley with high mountains all around and no sight of the airport until the last moment. Here is a cut of a map with the approach paths:

Approach to runway 15, marked in red, is worse in this regard. The ridge is rather close to the airport, so the final turn usually ends over the runway threshold. The wings get level with 30–50 ft (10–15 m) remaining only (here's a video). The approach to runway 33, marked in blue, allows a bit more of a straight final, but not by much. In either case the aircraft must emerge from the turn with correct altitude, speed and rate of descent. So the pilot has to know landmarks in the valley and how to judge correct approach profile by them. The approaches also often involve turning around higher in the valleys which again must be done by landmarks at places where it is known to be possible. It is this knowledge pilots have to demonstrate before they can attempt the approach (as pilots in command).
There are other airports where pilots have to receive special training to be permitted to fly there, for example the Samedan Airport near St. Moritz in Switzerland, which is similar mix of high altitude, high mountains around and visual approach, though it's still a lot easier as the airport is visible from much greater distance.
There is however nothing similarly difficult on Princess Juliana Airport. It appears approaches to Princess Juliana are only flown to runway 10 and these are over flat sea and flat beach. The runway is visible from great distance and the approach is straight. The featureless water makes it slightly harder to judge height than solid ground, but that's what the approach lights (VASI/PAPI) and distance-altitude table are for (there is no ILS at TNCM, only VOR-DME). And there are many airports with approach over water, so it's nothing unusual for the pilots. If there was approach to runway 28, it would have to be off-axis to avoid the hills on the island, but it does not appear to be used at all.

The pilot, Marek Tůma, who ferried in and for first 3 months commanded the ATR-42-500 A5-RGH, wrote a 4-part report (2, 3, 4; unfortunately in Czech) about flying in Bhutan.
According to that the training involved:

Couple of hours on simulator (in Bangkok).
Then they were permitted to ferry the plane to Paro.
Flight as observers with the training captain who showed them all the relevant landmarks in reality.
Some practice circuits.

They couldn't fly with the training captain in the other seat, because they were ATR-42 pilots and the training captain flies A320-family (and possibly still has rating for the older BAe146, but not ATR-42).
He also wrote that while on early flights when temperatures are still low the performance is good, later in the day it becomes marginal and they often needed to follow the valley quite far before they managed to climb above the mountains. Careful planning and weight and balance calculation was always necessary.

There is no ILS at TNCM - VASI lights only.

@J... true; I'll fix it.

Do we even dare ask what a go-around procedure for Paro is like?

@DJClayworth: Go-around procedure is no different from take-off procedure: climb up the valley up to the turning point.

@DJClayworth: There are other airports where landing is only one way and take-off is the opposite way and go-around is not an option beyond certain point, for example Tenzing-Hillary Airport at Lukla. But Paro allows both take-off and landing in both directions, so go-around is always possible.

This is really two questions

Why does Paro need special certification?
Why doesn't Princess Juliana need special certification?

I'll answer both, which I think answers your overall question about "Why does Paro need special certification but Princess Juliana doesn't?"
Why does Paro need special certification?
You've mostly answered this, it's because it's high up and in challenging terrain.

Less dense air at higher altitude requires a higher groundspeed on landing
The nature of the valley means there are almost constant, unpredictable gusty crosswinds. Nasty at any airport, but worse here due the terrain
The runway is short considering the terrain - it's not a short runway per se, but it increases the chance of needing to go around, which is tricky
It's very hard to go around compared to most airports - you need to know exactly where you're flying, rather than just maintaining runway heading and climbing out until given other instructions
You're in mountainous terrain (lots of things to crash into!)
The approaches are visual - added to the fact it's a difficult approach in the first place. The lack of ILS makes landing harder, you don't know if you're on the glideslope or not
And this has been covered by the other points, but it's worth repeating.... There are 5000m high mountains all around it, dramatically limiting approach and escape options

There's real no question that Paro is a difficult airport to land at: it requires an unusual approach, special awareness, a higher than normal level of skill and is very unforgiving.
Why doesn't Princess Juliana need special certification?
Because although the videos look very dramatic, simply put, it's not very hard to land at. The runway is short compared to most international airports, but it is long enough. Once the runway is beyond the minimum required for an aircraft, it's long enough and that's all there is to it. A longer runway may in theory require fewer go-arounds, but a "long enough" runway doesn't make landing there hard
Other than the runway length which, as just described, isn't actually a problem, there's nothing too difficult about it:

It's got nice, open approaches at each end
Clear glideslopes
It's at sea level, maneuvering is about as easy as it gets
It's an Instrument approach, you can make it in almost any weather
There's loads of time/space to make a missed approach and go around
There are no 5000m mountains around it, just lots of sea - and if you crash into the sea, you would have crashed into the ground anywhere else, so this isn't any more difficult than any other airport

It's not the easiest airport ever to land at, but it's not unusually difficult... although it certainly looks very dramatic, with the videos of Airliners sweeping over the top of a beach and road. The important thing to note is that the beach and road are both well below the glideslope - aircraft only really care about obstructions near or above the regular glideslope.
Although that beach approach looks crazy it actually poses no problems whatsoever for an aircraft - the jets are still comfortably on the glideslope: they don't care if the last section before the runway is grass, sand, a road etc, they were always going to be at that altitude.

You since edited the question to ask how they get this certification - you'd have to go and work for Druk Air (Royal Bhutan Airlines). Until recently they were the only carrier who flew into or out of the airport, and they work with the Bhutan government to certify pilots.

2 very great answers! was hard to choose the one to tag as answer, choosed the one with more upvotes!

I'm not so sure about "nice open approaches at each end". From Google Maps it looks like there's a 250 m ridge about 2.5 km from the threshold of runway 28. (The other answer indicates there are no approaches in that direction).

@HenningMakholm: Indeed, it seems at TNCM runway 28 is not used at all. I tried looking up approach plates and all of them only mentioned approaches to runway 10.

It's not used simply because prevailing winds make 10 a good option almost all the time, and there's no need to go over the hills - as far as I'm aware 28 does have a 3 degree (ie standard) glide slope available though if it was wanted (that said, I wouldn't bet my house on it)

If the elevations at Google Maps can be trusted, a glide path flatter than about 6° would pass through the hills east of the lagoon.

Quite possibly, I just assumed I'd landed on both sides to be honest, I hadn't thought about it too hard! Either way, it's still got one excellent approach :p

In open air I'd agree with you, but TAS/ground speed are important when landing. In isolation they aren't a huge deal, but taken in combination with the rest they add to an already tricky approach. Perhaps I should have stated that higher altitude requires a higher ground speed on landing, but the point is essential valid and should be taken with the whole post

authors: Игорь Сенчакович


text:
How can an airplane descend faster than a free-falling roll of toilet paper?
Watching this video, I was wondering, does the Toilet paper have this much lift, because I think the descent speed of the Airplane is not that much?

I don't think that a parachute-plane can catch up with a person in
free-fall?
Can somebody explain me physical how this maneuver works?

powered dive (nose is down) and a high-drag object -> kinda obvious

Ahhhh, there's nothing quite like littering from however many thousand feet.

Falling unrolled toilet paper is very light for its surface area and probably has a terminal velocity of not much more than 1 m/s or 200 feet/minute, which should be easily beatable by a small aircraft even without particular acrobatics.

I've actually had a parachute-plane pass me in free-fall when I was the last jumper out the door.  :)

"the descent speed of the airplane is not that much". The speed has nothing to do with that. What counts is the acceleration, because a free falling roll is accelerating at 1g, therefore the question is: Can an airplane accelerate more than gravity? The answer is it can, for a short time (maintaining a constant acceleration means reaching an infinite velocity). See this. "0-G" flights are done at 350 kt max, no big deal. Any bit more thrust and you are in the paper roll case.

"I think the descent speed of the airplane is not that much"
I think you are wrong.  Airplanes can descend very rapidly when needed.
The airplane is aerodynamic, meaning it slices through the air nicely, whether it is flying straight-and-level, or aiming straight for the ground.  So its free-fall speed is much higher than that of a roll of paper, which will have considerable wind resistance.
In addition, the airplane has a propeller, which adds force.  When in a dive, the airplane has gravity plus the force of the propeller taking down.  But the roll of paper only has gravity.
I expect that in a full dive, the airplane could probably exceed a 10,000 FPM descent, or around 120MPH, which is around the terminal velocity of a skydiver.
(pulling out of a full dive safely is not easy, however).
The roll of paper will obviously and intuitively be slower than a skydiver.
I estimate it to be no more than 2,000 FPM, or about 20 MPH. (and probably a bit less)

(edit: In the comments, Henning Makholm suggests that a paper roll may only fall at 200 FPM. That is less than 3 MPH, which seems a bit slow to me.   A slow descent rate for a Cessna when approaching an airport is 500 FPM.)

The airplane does not even need to enter a full dive to be faster than the paper. It could probably catch the paper with a nice, gentle 2,500 or 3,000 FPM descent.

The speed depends on how much of the roll has become a streamer. I think your 2,000 fpm estimate is reasonable based on the linked video, maybe just a bit high. As it unrolls it will probably slow towards 200 fpm.

Most planes can't descend at 10,000 ft/min because they would exceed their maximum design speed. Fast emergency descent in an airliner may be around 8,000 ft/min and that requires deployed spoilers.

@JanHudec:  I don't understand? 10,000 FPM is 113MPH, which is well within the Vne of most planes. I understand they cannot do 10,000 FPM in a normal attitude, but if you've got the altitude and point the nose at the ground, Vne does not seem to be the problem.  The problem would be the load-limit when you try to pull out of the dive.  Am I missing some other aspect?

@abelenky: You need to stabilize the speed. Just diving will get you to 10.000 fpm, and the airplane will be intact to this point. But, lacking adequate drag devices, it will continue to accelerate and flutter soon after. Jan is right, too much descent will not be possible in a stationary way which includes a safe landing after having stopped the descent.

I think the core point is that it is trivially easy for any plane to catch a roll of paper.  Whether the max descent speed is 10,000 or 4,000, it is far faster than the falling speed of the roll.

@JanHudec You're confusing "can't" and "shouldn't". It'll be able to exceed its maximum design speed by some margin before coming apart.

@ceejayoz If you chuck a typical GA piston single airplane into a vertical dive at 10,000 feet per minute (just shy of 100 knots) you could very easy to overstress the airframe and tear the wings off pulling out of the dive. (Presumably you've already got some forward speed when you enter the dive, so you'd hit 100 knots pretty quickly too!) That said, you don't need to go that fast to catch up with toilet paper: The MTO Sport Autogyro's max speed is only about 100 knots & it easily cut a streamer several times.

As an example of fast descent speeds, take SZD-50-3 Puchacz with Vne 215km/h. Full spoilers extended it can't exceed that speed, meaning that you can point your nose directly to ground and it will descend 215km/h or 11756fpm


text:
Where do flight sims get their data on aircraft flight characteristics?
Flight sims offer very realistic simulations of how a particular aircraft feels, claimed by pilot interviews on youtube.
But how do sims get their data?
First, does all this data even exist, i mean companies have data on how the aircraft changes control for example, due to some wind turbulance, or the slight turn of the steering?
Second, how do companies get this data? Particularly for fighters.
Third, how do they manage to offer such a realistic experience?
Are they in direct communication with the aircraft companies / goverments?
Isn't data like this confidential?

Re your third subquestion:  Is it realistic?  Has anyone trustworthy vouched for that?

Are you talking about home desktop simulators or professional simulators used to train pilots?

Related to professional simulation and before the sim can be used for training, authorities have strict regulations. They use the so called QTG's in order to certify a sim. ‘Qualification test guide (QTG)’ means a document designed to demonstrate that the performance and handling qualities of an FSTD are within prescribed limits with those of  the aircraft, class of aeroplane or type of helicopter and that all applicable requirements have been met. The QTG includes both the data of the aircraft, class of aeroplane or type of helicopter and FSTD data used to support the validation.

See the link for more info: https://www.easa.europa.eu/certification-specifications/cs-fstda-aeroplane-flight-simulation-training-devices

If you talk about certified FFS or FTD, each plane is made up of two main data sources:

The engineering data given by the aicraft manufacturer to the training device manufacturer. This data package contains mainly flight model and system description
The avionics data/software given by the company that developed the avionics for that particular plane

These data are confidential because it may contain sensitive data relating to military technologies and require a lot of effort to create and verify: for this reason it is a very expensive product that aicraft manufacturers sell to training device manufacturers. By itself, even JSBSIM or FlightGear or Prepar3d are realistic simulators: flight mechanics equations are "open source", however the difference is in the flight model of the plane.
An additional comment on flight models: they are made of equations and parameters that have been confirmed by the aircraft manufacturer through CFDs, Tunnel data and Flight test data. Further to this, there are a series of objective tests to verify that simulators behaviour matches the actual Flight test data

It comes from a few places and it depends on the type of simulator you are talking about, while the data is not necessarily "confidential" I would call it proprietary although much of it is actually out there:
The Public Domain: Home simulators like X-Plane offer the ability to build your own aircraft models and there are many readily available for sale. People may build these planes experimentally or based on the associated POH information. In many cases the airfoil information for light singles like the Cessna 172 is fairly readily available since its based on a specific NACA airfoil.
The aircraft companies: Since a great deal of training occurs in D-Level simulators these days (because its cheaper than burning Jet-A) the aircraft manufacturers may also build simulators for the real aircraft they build in this case they have the engineering data on hand to build the models.

A great deal of the "experience" also has to do with things that have nothing to do with the aircraft flight model. Things like weather simulation, graphics, airport markings, radio chatter, cockpit sounds, button availability, instrument response and avionics functionality. When I fly my sim its just as important to me that I can simulate the same GPS unit (Garmin 430) that I fly with as is the ability for the 172 to fly like it does in real IFR conditions.


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How does an aircraft turn while taxiing?
I know that an aircraft uses its own power (thrust) while taxiing to move forward. But how does it turn?

Do the front wheels pivot?
Do you simply apply more power to the left engine if you're trying to make a right turn?

If you do apply power to turn, how much power? Wouldn't it tip over the plane? And how do you do it on a single-engine or prop aircraft?

Definitely related, @fooot, but not duplicate. This question doesn't differentiate between "small" and "large" craft, nor have the exclusion of the tiller. Describing the operation of the tiller would make an excellent addition to an answer for this question.

Well we already have a question about large aircraft too...

I vote to re-open the the question as neither of the linked questions or answers properly address free castering nosewheels which are steered by using differential braking and/or differential power. Small aircraft like the Grumman AA-1 and AA-5, and larger aircraft like the Consolidated PBY-5A and B-24, all use free castering nosewheels. I am sure their are many other examples.

@MikeSowsun I think your point should be emphasize in the question so that it is clear it is not a duplicate.

Primarily steering is accomplished in two main ways:

Steerable nosewheels - Usually limited to tricycle undercarriage, and usually controlled using the same left/right pedals as control the rudder in flight
Using the rudder itself - Often associated with the traditional undercarriage (tail draggers to some). In this case the rudder works on the ground in much the same way as it does in the air - ie, deflecting the rudder pushes the tail in the opposite direction, thus causing the nose to pivot in the required direction.

In addition, steering can be augmented in two ways

Differential braking - often the left and right main undercarriage have their own deferentially controlled brakes. These are usually controlled by "hats" on the top of each rudder pedal. By applying greater braking pressure to, for example, the left wheel will cause the aircraft to pivot more around that wheel causing a left-turning tendency.
Differential thrust - in a similar vane to above, greater thrust applied to the left engine will cause a  right turning tendency.

steerable nosewheels: does that mean that when you use the rudder pedals while taxiing the rudder and wheels turn? or only the wheels do?
using the rudder itself: meaning you use the air to turn? how effective is this? don't you need high speed for the rudder to make a difference? (sorry I'm not very familiar though, that is just a general observation)

@majidarif - Both the rudder and the wheels turn in the case of steerable nosewheels, Yes, the rudder uses the airflow to make the aircraft turn on the ground - a surprisingly low, however not insignificant, amount of speed is required to make this work - however it's usually in conjunction with differential breaking.

Oh, one thing I should have mentioned is that its not ground speed so much as airflow speed which makes the rudder work on the ground. The propeller is providing that airspeed, not movement over the ground.

I have an edit pending review, but note that "breaking" is very different than "braking".

@FredLarson - lol, thanks for spotting my awful spelling there.

There are two major systems that are used to turn aircraft on the ground:

Steerable nose wheel.The wheel moves like on a car.
Differential braking (generally only small aircraft).
The nose gear is free castering. The pilot eases up on the brakes on one side or the other.

Not following what the image has to do with the answer, but in any case please cite the owner of the image. (Is that "Keith Morris"? - its not clear)

The images shows a free castering nose gear used with differential braking.


text:
What is this device on the nose of an MD-11?
In the following photo there is some sort of cover or opening (for an optical device I assume) on the nose cone.
What is this and what is the system behind it?

(link to source)

For a while I thought it was a very muddy plane (I have no idea how it would have gotten muddy) poorly photoshopped with... something else. It took a while to realize that was on the deicing pad.

Enhanced flight vision system
or a different angle
wiki says:

An Enhanced flight vision system (EFVS, sometimes EVS) is an airborne system which provides an image of the scene and displays it to the pilot, in order to provide an image in which the scene and objects in it can be better detected.

Welcome to Av.SE!


text:
How do you get an "FWC 1+2 FAULT" warning, if at all, on the Airbus A320?
ECAM messages are generated through DMC, which is from FWC and SDAC. The FWCs are responsible for ECAM warnings while the SDACs are for ECAM SD and ENG params. (DSC-31-05-30)
My question is: How would you know you have a dual FWC failure if there is no FWC to provide you with warnings anymore? There IS a warning FWS FWC 1+2 FAULT in FCOM which is not inhibited in any of the flight phases. Is this a warning that will never be triggered?
Additional: I'm aware that ECAM Memo can be used as a source of confirmation since Memo also fails when both FWCs fail. But I'm looking for a more "official" source to confirm if I have no FWCs.
Glossary:

DMC Display Management Computer
ECAM Electronic Centralized Aircraft Monitor

SD System Display

FWC Flight Warning Computer
FWS Flight Warning System
SDAC System Data Acquisition Concentrator

That's almost enough TLAs for the Army!

For those who don't speak Airbus, could somebody decode the acronyms, please?

@RalphJ I added a glossary.

@Bianfable Thanks. Is it possible to upvote an edit?  ;-)


text:
Which fighter jet is seen here at Centennial Airport Colorado?
These fighter jets landed at Centennial Airport Colorado today. What type of fighter jet are they?

These are F-18E Super Hornets, the single seat variant of the E/F Super Hornet.
The E/F variants are most noticeably different than their C/D counterparts by the square air intakes. When they are side-by-side the size difference is probably more noticeable.

The other thing I always look for is the little vertical stabilizers/fins ("fences") near the front of the wing in the non-Super Hornets: pic on wikipedia. They're easier for me to remember, because they come with a story: the Hornet originally didn't have them, but field testing revealed vortices that would hit the tail stabilizers and damage them; the small fins fixed that. When they redesigned the Super, they took the vortexes into account from the start.


text:
What devices measure EPR & RPM on a turbofan engine?
What devices measure EPR & RPM on a turbofan engine?

RPM is measured by a device called a tachometer. In a jet engine often this will be an inductive proximity probe that is measuring a toothed wheel on the shaft.
EPR is measured by comparing two static pressure sensors, one at the inlet and one at the propelling nozzle discharge, and taking the ratio. There are many different types of these. Many common ones will have a flexible membrane or diaphragm of some kind. Under pressure the membrane deflections and then you use some kind of deflection measurement.
These types of sensors are very common in many applications besides just jet engines. A little research on the internet will show you lots of details about how they are constructed and how they work.


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What is the difference between axial compressor blades and centrifugal compressor blades?
Is there a particular difference?  The way they're overhauled is the same ? (I mean do we use the same overhauling methods ?)

The blades are shaped completely differently. Typically a centrifugal compressor is one solid piece that looks like a turbocharger and an axial compressor is a flat disk that looks like a fan with individually manufactured blades inserted, though axial compressor disks with integral blades "blisk" is starting to be used. Here are compressor pics that show how they are used:
Two stage radial/centrifugal compressor circled (with a three stage axial turbine following)

Fifteen stage axial compressor

A radial compressor can usually generate higher pressure in a single stage so it's usually simpler, while an axial compressor is easier to stack in multiple stages to get much higher pressure ratios.

The main difference is in how they operate, vs how they are maintained. Flow through a centrifugal compressor is turned perpendicular to the axis of rotation, while air in an axial compressor flows parallel to the axis of rotation.

Axial blades are airfoils that compress air by forcing it aft into a converging space via downwash the same as a wing generates lift by downwash.  Efficient, but sensitive to angle of attack and aerodynamic stall, like a regular wing, so therefore sensitive to flow disruptions.
A centrifugal compressor is spinning duct that forces air into a converging space purely by centrifugal force imparted to air within it as it spins.  Less efficient, but relatively insensitive to flow disruptions and way easier to make.

Axial blades do not have to be airfoils.

Do you know of a turbine engine with flat ones?


text:
What is the plus or minus limits of Jeppesen Approach Chart Speed Restrictions
I couldn't find any information on this topic.
Do Speed Restrictions depicted on Jeppesen Approach Charts have plus or minus limitations for any restriction we see on the charts? Do we have to exactly keep that speed? Not even a 1 knot boundary?

The fact that the charts are published by Jepp or any other entity is a red herring, IMO. The procedures depicted on the charts are created by a given country's ANSP and you will have to check that country's guidance for what their tolerances are.

@757toga Actually, i thought the answer would be general including all charts. But, you are right. Effect of deviation from restriction probably differ from Approach Chart to SIDs or STARs. Since I couldn't find any sources of information on this I am open to all kinds of information :) Thanks in advance.

Are you asking about maximum speed restrictions? I don’t think I’ve ever seen a chart with a mandatory speed restriction.

@757toga, thanks!

Speeds in the chart, along with altitudes and (when part of the procedure) headings, are assignments by ATC, much like a controller directing an aircraft to "maintain 3,000' and fly heading 180."
Obviously, flying at 3,001 feet and heading 181 isn't likely to be considered a violation of the clearance -- nobody out there would still be flying if it were.  Tolerances are specified elsewhere, not in Jeppesen charts, and as @randomhead pointed out in the comments, Jepp simply reproduces what each nation gives them, in a standard format.
Typical ATP tolerances are plus/minus 10 degrees, 100 feet, and 10 knots. Since most instrument procedures (once the training is complete) are flown with a flight director or autopilot (and, often, auto throttles), the expectation is that you set the 250 knots (or whatever speed is called for) in the system, and you (or the automation) strive to hold that speed.  If you get off of it a little bit, you make the appropriate correction.  If you're assigned 250 and you're chugging along at 265 and not correcting, then you're not doing what you should be.
Whether you'll get called out on that deviation or not is highly dependent on context, who's watching, and what equipment they have to see exactly what it is you're doing.  If "your" 250 knots is significantly faster or slower than other aircraft on the same arrival also doing "250 knots" then ATC will probably notice; if they don't have ADSB reporting your exact speed and you're the only aircraft out there, the controller will probably assume there's a headwind or tailwind affecting your groundspeed and probably won't worry much about it.
Slight related:
There's an old story about a particular airline that was known for going pretty fast back in the day, and a particular captain who flew around fast all the time.  He's on an arrival, flying at his usual speed of heat, and ATC asks his airspeed.  The FO replies with their speed, and they're told to slow to 280 knots.  The captain does no such thing, and a few minutes later they're told to slow to 250 knots.  The FO dutifully reads back the clearance, and the captain changes nothing.  Finally ATC asks them to "say airspeed," to which the captain tells the FO to "Tell 'em we're doing 250."  The FO isn't real keen about lying on the radio, but the captain is in charge...
"The captain says we're doing 250, sir"
The captain's head promptly explodes, with a great tirade of that's not what I told you to say, etc etc.  The controller calmly replies, "well, your 250 is faster than {other airline}'s 300 knots, so your captain can either slow down, or I'm going to have to give you vectors out over North Dakota for spacing."
I have no idea if they actually slowed down enough to avoid the vectors, or not.

Thanks! Great story and an example of CRM maybe. :) Where can I find those tolerances?  ICAO Annexes?


text:
What is this twin engine propeller aircraft flying for Garuda airlines in Indonesia in 1983?
Twin propeller small civil aircraft flown by Garuda Airlines Indonesia in 1983.
aZxGQ.jpg

Looks to be a Shorts Skyvan.  Sometime called the ‘Flying Shoebox’.
https://en.m.wikipedia.org/wiki/Short_SC.7_Skyvan

Not Garuda.. Its in Pelita livery. This company did a lot of charters for the oil industry.\


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The standard parts used on STC projects should be Indicated conform to FAR regulations？
The standard sleeve accept by Boeing SWPM, it conform to "AMS-DTL-23053/5 class 1".
However, when we use this product in STC project, we are required to prove that it meets FAR25.853(a) by DER.
Have you ever encountered a similar situation? What is the accreditation procedure of standard parts in STC project?


text:
Do I need to keep my foreign based PPL after passing an FAA instrument checkride?
I have a foreign based PPL (PPL issue on the basis and valid only as long as my foreign PPL is valid). I'm going to go for an instrument rating checkride very soon.
Assuming I pass the checkride successfully, does my license become valid regardless of my foreign one or do I still need to keep both?
I lived in the US for the past 10 years and I am a US citizen.

Adding an instrument rating doesn't change the fact that your FAA private certificate is foreign-based. The IR is an add-on to a pilot certificate, it isn't a certificate itself. If you don't keep your foreign license current then you can't fly on your FAA foreign-based certificate.
To get rid of your foreign-based certificate, you can either do a regular FAA private checkride (including the written exam) or get an FAA commercial certificate (which replaces your private one). In both cases you'll also need an FAA medical to replace your foreign medical.
Source: I did an FAA IR while holding a foreign-based private certificate. I later did the private checkride to get a 'full' FAA private certificate. See this answer for a few additional details on going from foreign-based to 'full'.

When your instrument is added to your FAA Restricted (Foreign Based) certificate you will have the "Instrument-Airplane (US Test Passed)" added to this certificate. Reference: FAA 8900.1
If you later pass a standard FAA Private/Commercial certificate the Instrument US Test passed will transfer to this new certificate. You will still maintain your Restricted certificate. In some cases this is beneficial. But generally, you will not need your FAA Restricted certificate anymore.

Including links to source material is a great start. Quoting the relevant sections is even better because links die.


text:
What is the height requirement for pilots in the Philippines?
I am not an airline pilot nor do I work in the industry but I'm looking forward to. I live in the Philippines, a part of South East Asia.
My question is: what is the current minimum height requirement in the Philippines to be a private airline or commercial airline pilot?
I was at a Aviation School seminar a few months ago and one of the guest asked the host if height still mattered and the host answered "not anymore because airplane pilot seats are now adjustable". That didn't really convince me because they might be biased considering they are looking for students.

I am roughly about 5'3".

welcome to aviation.SE. The current requirement is on topic, but how you'd project the requirement will change in the future is not (we don't do speculation here).
Are you interested in the requirement in the Philippines or somewhere else?

@Federico Thank you. I am interested in the requirement in the Philippines. :)

There's no minimum height stated in the Philippines Civil Air Regulations (section 2.10.2.2) for any class of medical (you need a class 1 medical for a commercial license). However, Philippine Airlines apparently requires pilots to be at least 5'4" / 162cm.

Thank you. Would you know the requirements from Cebu Pacific Airlines? That is a budget airlines in the Philippines.

@majidarif You're welcome! I have no idea about Cebu, unfortunately

Cebu! Sorry, my kids watched that incessantly, and it's still stuck in my head, 15 years later... :)

I just measured my height with a tape measure. It was 161.5cm. I'm 23. Can't even get the height requirement for PAL. :D


text:
Where can a 300lb person get a spin endorsement in Miami?
I'm in Miami Working on my CFI, I'm at the level of trying to get my spin endorsement. The problem is I'm 6'2" and 300lb, so I need your help.

Paraphrasing a classic movie ... "We're gonna need a bigger plane"

So what's the actual question?

Find a spin-training class that uses something bigger than a 150 Aerobat. Here in WI there is a guy conducting upset training in a E33c Bonanza.

where can I do my spin endorsement in a big plane @GdD ?


text:
Why is a rectangular wing planform less efficient than others?
I read somewhere that a rectangular wing is inefficient compared to other wing planforms. Can someone clarify why this kind of wing planform is inefficient compared to other planforms and what causes this "inefficiency"?

I read this post, but still I don’t know what causes this „unefficiency”. More drag? If yes, I will be more than happy to know why there is more drag on this wing planform.

So the reason is just non-elliptical lift distribution?

@konrad Can you please post the link of the article that you have read? So we can give a clear answer based on the article you have read

The inefficiency is the result of a comparably high weight in relation to the possible lift. However, for small aircraft that disadvantage is not very pronounced (this is true especially for braced wings and biplanes) and is outweighed by very favorable stall characteristics. Also, a rectangular wing is very easy to build. Compare with what has been built so far - many competitive small aircraft and most biplanes use a rectangular wing. Since they often cruise at speeds much above their best range speed, induced drag optimisation is of minor importance in those designs.
A better planform has more chord at the root and less at the tip: Such a trapezoidal wing can be built lighter. If the root has more chord, the spar can be made thicker, and if the area at the tips is smaller, less bending moment is created for the same lift. Bracing takes care of the root bending moment, but in cantilevered monoplanes the rectangular wing loses most of its benefits. A taper ratio of 0.7 will still leave enough stall margin at the tips when combined with some washout.
Especially large aircraft tend to have even smaller taper ratios because they concentrate most lift near the root wich makes their wings more efficient. Even though their induced drag coefficient might be higher than that of an elliptical wing, their overall induced drag is lower because of the comparably low wing mass which lowers the overall lift requirement.

Yes, the requirements for structural efficiency are a bit different from aerodynamic efficiency. broadly speaking, taper helps both, but the details are rather different.

Thanks for the answer! Another great explanation from you.

For the same wing span, an elliptical wing planform is the most aerodynamically efficient compared to any other flat wing planform because it has the lowest induced drag. Note that we are comparing only aerodynamics here. Things get much more nuanced once you couple structural weights, stability & control for a global efficiency (also see @Peter's answer).
1. Induced drag
So restricting to aerodynamics, elliptical wing planform is the most efficient because it has the lowest induced drag. Induced drag is produced because wings have finite span, and therefore one section of the wing distorts the flow on another section, creating downwash. This downwash distorts the lift vector on each wing section, thereby converting what otherwise would be lift into drag.
2. Downwash
Now that you understand induced drag has to do with downwash on each span section, you must appreciate that the distribution of downwash over the span is important to the induced drag generation. Distribution of downwash is dictated completely by the lift distribution over the wing (and vice-versa), which is in turn, dictated by the shape of the wing planform.
3. Lift distribution
For an elliptical wing planform, we can prove that it also generates an elliptical lift distribution. When you do the math of integrating all the sectional induced drag from the downwash and sectional lift, elliptical lift distribution has the lowest induced drag.
The following figures show the distributions of elliptical wing, rectangular wing (taper = 1) and tapered wing (taper = 0.5), with aspect ratio 8 and all producing a total $C_L=0.4$. Here, Ref Cl is the actual lift coefficient distribution that we've talking about, but multiplied by span length; Local Cl is the lift coefficient produced at each wing section, as if it's standalone airfoil; $\alpha_i$ is the downwash distribution in deg. The data are generated from Lifting Line Theory.

As you can see, elliptical distribution maintains a constant downwash, compare that to a wider and more varied one for a rectangular wing. Also, a taper of 0.5 gets you fairly close to the elliptical lift and downwash distributions, especially when you consider the $\frac{C_L}{C_{D_i}}$, which is 62.8 for elliptical and 61.8 for tapered.

Thanks a lot! Very comprehensive and easy to understood explanation.

It'a a bit misleading to only present results for straight wings without washout when in reality most rectangular wings use at least some washout.

"Local Cl is the lift coefficient produced at each wing section, as if it's standalone airfoil" doesn't make sense to me. If we just looked at the 2d airfoil at each section then this would show a curve corresponding to an ellipse for the elliptical wing, a flat line for the rectangular wing and linearly decreasing line for the tapered wing, no?

@xnor What doesn't make sense to you? I don't understand the second part of your comment. What's "a flat line" for rect wing and "decreasing line" for tapered wing?

@JZYL flat line as in constant across y, decreasing line as in linearly decrease with y.
It's just not clear what Ref and Local Cl are, and the descriptions don't help. You also say Ref Cl is Cl multiplied by span length, but span length is a constant and the same for all three cases.

@xnor What's constant across y? Neither local Cl nor Ref Cl nor downwash is constant across y for the rectangular wing. The only that is constant is the chord length. The "multiplied by span" part is just so that Ref Cl and Local Cl have the similar magnitudes (otherwise one would be normalized with respect to wing area, while the other normalized to wing chord); it doesn't change the shape or conclusion.

The fundamental issue is the behaviour at the wing tip.
On a rectangular wing the high pressure beneath and the low pressure above cause air to spill up round the tip and spiral backwards in a wingtip vortex. This both lowers the pressure difference, reducing lift near the tip, and loses energy to the vortex, increasing drag. Both these effects reduce overall efficiency.
If the tip is made smaller while keeping the wing span and area the same, for example by tapering the wing or making it elliptical, then the tip losses and the inefficiency are also reduced.
A more detailed explanation gets more complicated, but I am not sure you want all that.

Thank you! Now it is clear. If you have more detailed explanation I'll be more than happy to read it and fully understand the topic!

Proper washout will make your point moot. Tip losses are identical for identical circulation distributions.

@PeterKämpf Lots of technical variations make the point moot; a well-designed rectangular wing can be more efficient than a badly-designed elliptical one, but that does not affect the basic other-things-being-equal situation.